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Finding the Third Proportional to 12,774 and 19,829

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Solution

The third proportional to 12,774 and 19,829 is: 30,780.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,774 : 19,829 = 19,829 : x
  2. Step 2: Convert to fraction form
    12,774/19,829 = 19,829/x
  3. Step 3: Cross multiply
    12,774x = 19,829 × 19,829
  4. Step 4: Simplify right side
    12,774x = 393,189,241
  5. Step 5: Solve for x
    x = 393,189,241/12,774
  6. Step 6: Final answer
    x = 30,780.43

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.